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mathematics
calculus early transcendentals 9th

Physics For Scientists And Engineers A Strategic Approach With Modern Physics 3rd Edition Randall D. Knight - Solutions

Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state.a. 1s22s22p5b. 1s22s22p63s23p64s23d104p
In a multielectron atom, the lowest-l state for each n (2s, 3s, 4s, etc.) is significantly lower in energy than the hydrogen state having the same n. But the highest-l state for each n (2p, 3d, 4f, etc.) is very nearly equal in energy to the hydrogen state with the same n. Explain.
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state.a. 1s22s22p53sb. 1s22s22p63s23p64s23d2
In Figure Q 41.12, a photon with energy 2.0 eV is incident on an atom in the p state. Does the atom undergo an absorption transition, a stimulated emission transition, or neither? Explain. E (eV) s state 3.0 p state 2.0 Photon s state 0.0
Show that hc = 1240 eV nm.
What is the electron configuration of the second excited state of lithium?
An electron accelerates through a 12.5 V potential difference, starting from rest, and then collides with a hydrogen atom, exciting the atom to the highest energy level allowed. List all the possible quantum-jump transitions by which the excited atom could emit a photon and the wavelength (in nm)
a. Is a 4p → 4s transition allowed in sodium? If so, what is its wavelength (in nm)? If not, why not?b. Is a 3d → 4s transition allowed in sodium? If so, what is its wavelength (in nm)? If not, why not?
An excited state of an atom has a 25 ns lifetime. What is the probability that an excited atom will emit a photon during a 0.50 ns interval?
1.0 × 106 sodium atoms are excited to the 3p state at t = 0 s. How many of these atoms remain in the 3p state at(a) t = 10 ns(b) t = 30 ns(c) t = 100 ns?
A hydrogen atom is in the 2p state. How much time must elapse for there to be a 1% chance that this atom will undergo a quantum jump to the ground state?
1.0 × 106 atoms are excited to an upper energy level at t = 0 s. At the end of 20 ns, 90% of these atoms have undergone a quantum jump to the ground state.a. How many photons have been emitted?b. What is the lifetime of the excited state?
1.00 × 106 sodium atoms are excited to the 3p state at t = 0 s. At what time have 8.0 × 105 photons been emitted?
A 1.0 mW helium-neon laser emits a visible laser beam with a wavelength of 633 nm. How many photons are emitted per second?
In LASIK surgery, a laser is used to reshape the cornea of the eye to improve vision. The laser produces extremely short pulses of light, each containing 1.0 mJ of energy.a. There are 9.7 × 1014 photons in each pulse. What is the wavelength of the laser?b. Each pulse lasts a mere 20 ns. What is
A laser emits 1.0 × 1019 photons per second from an excited state with energy E2 = 1.17 eV. The lower energy level is E1 = 0 eV.a. What is the wavelength of this laser?b. What is the power output of this laser?
a. Draw a diagram similar to Figure 41.3 to show all the possible orientations of the angular momentum vector L(vector) for the case l = 3. Label each L(vector) with the appropriate value of m.b. What is the minimum angle between L(vector) and the z-axis? If m = 2, L lies somewhere on the surface
There exist subatomic particles whose spin is characterized by s = 1, rather than the s = 1/2 of electrons. These particles are said to have a spin of one.a. What is the magnitude (as a multiple of h) of the spin angular momentum S for a particle with a spin of one?b. What are the possible values
A hydrogen atom in its fourth excited state emits a photon with a wavelength of 1282 nm. What is the atom’s maximum possible orbital angular momentum (as a multiple of h) after the emission?
A hydrogen atom has l = 2. What are the(a) Minimum (as a multiple of h)(b) Maximum values of the quantity (Lx2 + Ly2)1/2?
Calculate(a) The radial wave function(b) The radial probability density at r = 1/2 aB for an electron in the 1s state of hydrogen. Give your answers in terms of aB.
For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 0.010aB at distance(a) 1/2 aB(b) aB(c) 2aB from the proton?
Prove that the normalization constant of the 1s radial wave function of the hydrogen atom is (πaB3)–1/2, as given in Equations 41.7. A useful definite integral is
Prove that the normalization constant of the 2p radial wave function of the hydrogen atom is (24πaB3)–1/2, as shown in Equations 41.7. 1 R1,(r) = -rlag 1 ap -r/2ag R2,(r) 1 3 2ag 1 r R„(r) -r/2ag e V24ma, |2aB. 3
Prove that the radial probability density peaks at r = aB for the 1s state of hydrogen.
a. Calculate and graph the hydrogen radial wave function R2p(r) over the interval 0 ≤ r ≤ 8aB.b. Determine the value of r (in terms of aB) for which R2p(r) is a maximum.c. Example 41.3 and Figure 41.8 showed that the radial probability density for the 2p state is a maximum at r = 4aB. Explain
In general, an atom can have both orbital angular momentum and spin angular momentum. The total angular momentum is defined to be J(vector) = L(vector) + S(vector). The total angular momentum is quantized in the same way as L(vector) and S(vector). That is, J = √j(j +1)h, where j is the total
Draw a series of pictures, similar to Figure 41.22, for the ground states of K, Sc, Co, and Ge. 2p 2s %23 %23 1s Z = 5 B 1s°25 2p Z = 6 C 1s 2s°2p? Z =7 N 1s 2s°2p Z = 8 0 1s°2s°2p* Z = 9 F 1s 2s°2p° Z = 10 Ne 1s 2s°2p°
Draw a series of pictures, similar to Figure 41.22, for the ground states of Ca, Ni, As, and Kr. 2p 2s %23 %23 1s Z = 5 B 1s°25 2p Z = 6 C 1s 2s°2p? Z =7 N 1s 2s°2p Z = 8 0 1s°2s°2p* Z = 9 F 1s 2s°2p° Z = 10 Ne 1s 2s°2p°
a. What downward transitions are possible for a sodium atom in the 6s state? (See Figure 41.24.)b. What are the wavelengths of the photons emitted in each of these transitions? Energy (eV) 1 = 0 1 = 1 1 = 2 1 = 3 Ionization limit 5.14 eV 5- 4.51 4.34 4.11 5p 3.75 4p 3.19 6s 4.28 4.29 4d 4f- 5s 4
The 5d → 3p transition in the emission spectrum of sodium has a wavelength of 499 nm. What is the energy of the 5d state?
A sodium atom emits a photon with wavelength 818 nm shortly after being struck by an electron. What minimum speed did the electron have before the collision?
The ionization energy of an atom is known to be 5.5 eV. The emission spectrum of this atom contains only the four wavelengths 310.0 nm, 354.3 nm, 826.7 nm, and 1240.0 nm. Draw an energy-level diagram with the fewest possible energy levels that agrees with these experimental data. Label each level
Figure P 41.41 shows the first few energy levels of the lithium atom. Make a table showing all the allowed transitions in the emission spectrum. For each transition, indicatea. The wavelength, in nm.b. Whether the transition is in the infrared, the visible, or the ultraviolet spectral region.c.
Figure P 41.42 shows a few energy levels of the mercury atom.a. Make a table showing all the allowed transitions in the emission spectrum. For each transition, indicate the photon wavelength, in nm.b. What minimum speed must an electron have to excite the 492-nm-wavelength blue emission line in the
Suppose you put five electrons into a 0.50-nm-wide one dimensional rigid box (i.e., an infinite potential well).a. Use an energy-level diagram to show the electron configuration of the ground state.b. What is the ground-state energy of this configuration?
Three electrons are in a one-dimensional rigid box (i.e., an infinite potential well) of length 0.50 nm. Two are in the n = 1 state and one is in the n = 6 state. The selection rule for the rigid box allows only those transitions for which Δn is odd.a. Draw an energy-level diagram. On it, show the
a. What is the decay rate for the 2p state of hydrogen?b. During what interval of time will 10% of a sample of 2p hydrogen atoms decay?
An atom in an excited state has a 1.0% chance of emitting a photon in 0.10 ns. What is the lifetime of the excited state?
a. Find an expression in terms of τ for the half-life t1/2 of a sample of excited atoms. The half-life is the time at which half of the excited atoms have undergone a quantum jump and emitted a photon.b. What is the half-life of the 3p state of sodium?
In fluorescence microscopy, an important tool in biology, a laser beam is absorbed by target molecules in a sample. These molecules are then imaged by a microscope as they emit longer wavelength photons in quantum jumps back to lower energy levels, a process known as fluorescence. A variation on
An electrical discharge in a neon-filled tube maintains a steady population of 1.0 × 109 atoms in an excited state with t = 20 ns. How many photons are emitted per second from atoms in this state?
A ruby laser emits a 100 MW, 10-ns-long pulse of light with a wavelength of 690 nm. How many chromium atoms undergo stimulated emission to generate this pulse?
Two excited energy levels are separated by the very small energy difference ΔE. As atoms in these levels undergo quantum jumps to the ground state, the photons they emit have nearly identical wavelengths λ.a. Show that the wavelengths differ byb. In the Lyman series of hydrogen, what is the
What is the probability of finding a 1s hydrogen electron at distance r > aB from the proton?
Suppose you have a machine that gives you pieces of candy when you push a button. Eighty percent of the time, pushing the button gets you two pieces of candy. Twenty percent of the time, pushing the button yields 10 pieces. The average number of pieces per push is Navg = 2 × 0.80 + 10 × 0.20 =
Prove that the most probable distance from the proton of an electron in the 2s state of hydrogen is 5.236aB.
Find the distance, in terms of aB, between the two peaks in the radial probability density of the 2s state of hydrogen.
An atom in an excited state has a 1.0% chance of emitting a photon in 0.20 ns. How long will it take for 25% of a sample of excited atoms to decay?
The 1997 Nobel Prize in physics went to Steven Chu, Claude Cohen-Tannoudji, and William Phillips for their development of techniques to slow, stop, and “trap” atoms with laser light. To see how this works, consider a beam of rubidium atoms (mass 1.4 × 10-25 kg) traveling at 500 m/s after being
What is the electric potential energy of the group of charges in Figure EX 28.7? 2.0 nC 3.0 nC 3.0 cm 14.0 cm 3.0 nC
Show that 1 V/m = 1 N/C.
A proton moves along the x-axis, where an arrangement of source charges has created the electric potential V = 6000x2, where V is in volts and x is in meters. By exploiting the analogy with the potential energy of a mass on a spring, determine the proton’s oscillation frequency.
An uncharged parallel-plate capacitor with spacing d is horizontal. A small bead with mass m and positive charge q is shot straight up from the bottom plate with speed v0. It reaches maximum height ymax before falling back. Then the capacitor is charged with the bottom plate negative. Find an
The sun is powered by fusion, with four protons fusing together to form a helium nucleus (two of the protons turn into neutrons) and, in the process, releasing a large amount of thermal energy. The process happens in several steps, not all at once. In one step, two protons fuse together, with one
A thin spherical shell of radius R has total charge Q. What is the electric potential at the center of the shell?
An electric dipole with dipole moment p is oriented along the y-axis.a. Find an expression for the electric potential on the y-axis at a point where y is much larger than the charge spacing s. Write your expression in terms of the dipole moment p.b. The dipole moment of a water molecule is 6.2 ×
A sphere of radius R has charge q.a. What is the infinitesimal increase in electric potential energy dU if an infinitesimal amount of charge dq is brought from infinity to the surface of the sphere?b. An uncharged sphere can acquire total charge Q by the transfer of charge dq over and over and
A circular disk of radius R and total charge Q has the charge distributed with surface charge density η = cr, where c is a constant. Find an expression for the electric potential at distance z on the axis of the disk. Your expression should include R and Q, but not c.
What is the potential difference between xi = 10 cm and xf = 30 cm in the uniform electric field Ex = 1000 V/m?
What is the potential difference between yi = -5 cm and yf = 5 cm in the uniform electric field E(vector) = (20,000î - 50,000ĵ) V/m?
Figure EX29.12 is a graph of V versus x. Draw the corresponding graph of Ex versus x. V (V) 50 ( (cm) 3 -50- 2.
Figure EX 29.26 shows Q versus t for a 2.0 μF capacitor. Draw a graph showing UC versus t. Q (uC) 200 - t (s) 4 1 3
Capacitor 2 has half the capacitance and twice the potential difference as capacitor 1. What is the ratio UC1/UC2?
a. Which point in Figure P 29.33, A or B, has a larger electric potential?b. What is the potential difference between A and B? E = 1000 V/m В. 7 сm 3 cm con
The electric field in a region of space is Ex = -1000x V/m, where x is in meters.a. Graph Ex versus x over the region -1 m ≤ x ≤ 1 m.b. What is the potential difference between xi = -20 cm and xf = 30 cm?
The electric field in a region of space is Ex = 5000x V/m, where x is in meters.a. Graph Ex versus x over the region -1 m ≤ x ≤ 1 m.b. Find an expression for the potential V at position x. As a reference, let V = 0 V at the origin.c. Graph V versus x over the region -1 m ≤ x ≤ 1 m.
An infinitely long cylinder of radius R has linear charge density λ. The potential on the surface of the cylinder is V0, and the electric field outside the cylinder is Er = λ/2πϵ0r. Find the potential relative to the surface at a point that is distance r from the axis, assuming r > R.
What is the capacitance of the two electrodes in Figure P 29.58? Electrodes extend 1.0 cm into page. 2.0 1.0 mm mm 1.0 cm 1.0 cm
A parallel-plate capacitor is constructed from two 10 cm × 10 cm electrodes spaced 1.0 mm apart. The capacitor plates are charged to ±10 nC, then disconnected from the battery.a. How much energy is stored in the capacitor?b. Insulating handles are used to pull the capacitor plates apart until the
What is the energy density in the electric field at the surface of a 1.0-cm-diameter sphere charged to a potential of 1000 V?
You need to use a motor and lightweight cable to lift a 2.0 kg copper weight to a height of 3.0 m. To do so, you’ve decided to use a 1000 V power supply to charge a capacitor, then run the motor by letting the capacitor discharge through it. If the motor is 90% efficient (that is, 10% of the
The electric potential in a region of space is V = 100(x2 – y2) V, where x and y are in meters.a. Draw a contour map of the potential, showing and labeling the –400 V, –100 V, 0 V, +100 V, and +400 V equipotential surfaces.b. Find an expression for the electric field E(vector) at position (x,
What is the difference between current and current density?
2.0 × 1013 electrons flow through a transistor in 1.0 ms. What is the current through the transistor?
In an ionic solution, 5.0 × 1015 positive ions with charge +2e pass to the right each second while 6.0 × 1015 negative ions with charge -e pass to the left. What is the current in the solution?
A metal cube 1.0 cm on each side is sandwiched between two electrodes. The electrodes create a 0.0050 V/m electric field in the metal. A current of 9.0 A passes through the cube, from the positive electrode to the negative electrode. Identify the metal.
A 10-m-long wire with a diameter of 0.80 mm has a resistance of 1.1 Ω. Of what material is the wire made?
Figure EX 30.36 is a current-versus-potential difference graph for a material. What is the material’s resistance? I (A) 1. 04 50 AV (V) 100 2.
Figure P30.65 shows the potential along a tungsten wire. What is the current density in the wire? V (V) 3.0- s (cm) 30 0+
The electric field in a current-carrying wire can be modeled as the electric field at the midpoint between two charged rings. Model a 3.0-mm diameter aluminum wire as two 3.0-mm-diameter rings 2.0 mm apart. What is the current in the wire after 20 electrons are transferred from one ring to the
A metal wire connecting the terminals of a battery with potential difference ΔVbat gets warm as it draws a current I.a. What is ΔU, the change in potential energy of charge Q as it passes through the wire?b. Where does this energy go?c. Power is the rate of transfer of energy. Based on your
In Figure EX 31.3, what is the current in the wire to the right of the junction? Does the charge in this wire flow to the right or to the left? 4 V I 2Ω + 50S15 V
What is the potential difference across each resistor in Figure EX 31.6? 12 N 30 V 33 2
Two of the three resistors in Figure EX 31.13 are unknown but equal. The total resistance between points a and b is 200 Ω. What is the value of R? R 50 N R wwww ww a
What is the time constant for the discharge of the capacitors in Figure EX 31.28? 2 μF 2 μF 1kΩ 1 k2 ww
The corroded contacts in a lightbulb socket have 5.0 Ω resistance. How much actual power is dissipated by a 100 W (120 V) lightbulb screwed into this socket?
You have three 12 Ω resistors. Draw diagrams showing how you could arrange all three so that their equivalent resistance is(a) 4.0 Ω(b) 8.0 Ω(c) 18 Ω(d) 36 Ω
There is a current of 0.25 A in the circuit of Figure P 31.42. What is the power dissipated by R? 12 2 ww + 6 V 12 V R ww
What is the emf of the battery in Figure P 31.46? R ER 3.0 A 2.0 A 10 Ω
A 2.5 V battery with 0.70 Ω internal resistance is connected in parallel with a 1.5 V battery having 0.30 Ω internal resistance. That is, their positive terminals are connected by a wire and their negative terminals are connected by a wire. What is the terminal voltage of the 2.5 V battery?
The ammeter in Figure P 31.49 reads 3.0 A. Find I1, I2, and ε. 3.0 Ω 4.5 N ww- ww I, 2.0 Ω 9 V E 言& A) 3.0 A
A capacitor-charging circuit has a time constant of 40 ms. When the switch is closed, the initial current to the 50 μF capacitor is 65 mA. What is the capacitor’s voltage after 20 ms? Assume the capacitor was completely uncharged when the switch closed.
A proton is passing the origin. The magnetic field at the (x, y, z) position (1 mm, 0 mm, 0 mm) is 1.0 × 10-13 ĵ T. The field at (0 mm, 1 mm, 0 mm) is -1.0 × 10-13 î T. What are the speed and direction of the proton?
What currents are needed to generate the magnetic field strengths of Table 32.1 at a point 1.0 cm from a long, straight wire? Field source Field strength (T) Surface of the earth 5x 10-5 Refrigerator magnet Laboratory magnet Superconducting magnet 5 x 10-3 0.1 to 1 10
At what distances from a very thin, straight wire carrying a 10 A current would the magnetic field strengths of Table 32.1 be generated? Field source Field strength (T) Surface of the earth 5x 10-5 Refrigerator magnet Laboratory magnet Superconducting magnet 5 x 10-3 0.1 to 1 10
A 2.0-cm-diameter, 15-cm-long solenoid is tightly wound with one layer of wire. A 2.5 A current through the wire generates a 3.0 mT magnetic field inside the solenoid. What is the diameter of the wire, in mm?
Test instruments to measure magnetic field strengths are often based on the Hall effect. In one instrument, the “probe” is a 1.0-mm-thick, 6.0-mm-wide semiconductor with a charge-carrier density of 2.1 × 1021 m-3, much less than the charge-carrier density in a conductor. Passing a 60 mA
A spherically symmetric charge distribution produces the electric field E(vector) = (200/r)r̂N/C, where r is in m.a. What is the electric field strength at r = 10 cm?b. What is the electric flux through a 20-cm-diameter spherical surface that is concentric with the charge distribution?c. How much
The electric flux is 300 Nm2/C through two opposing faces of a 2.0 cm × 2.0 cm × 2.0 cm box. The flux through each of the other faces is 100 N m2/C. How much charge is inside the box?

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